Math 109 Practice Midterm I PDF

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Math 109 Sample Midterm 1 for Fall 2020...

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MATH 109 Indiviual Test # 1 – January 30, 2020 Time: 1 hour 20 minutes

Last Name:

Student #: V00

First Name: TURN CELL PHONES, ELECTRONIC DEVICES, ETC. OFF, AND REMOVE THEM FROM YOUR DESK. CELL PHONES MUST BE IN YOUR BAG AND NOT IN YOUR POCKET. Instructions: • The only calculators allowed on any examination are the Sharp EL-510R and the Sharp EL-510RNB. • No other aids are permitted. • This test consists of 20 questions and has 10 pages (Plus a BLANK page at the back of the test). – Questions 1 through 7 are multiple-choice questions. Circle your chosen answer in the test booklet and mark your choice on the provided bubble-sheet. The exact answer may not be present. If this is the case, choose the closest answer available. If the answer is exactly halfway between two options, choose the larger of the two options. – Questions 8-16 are short answer. Please write your final answer to each question in the provided answer box. Sufficient work must be shown for all questions, as we may disallow any answer which is not properly justified. If there is a calculation required for the problem, show the calculation. – Questions 17 through 20 are long-answer. Write your full answer in this booklet as indicated. Part marks will be awarded for these questions. Marks will be deducted for incomplete or poorly presented solutions. – Errors will not be ignored. If you have both a correct and an incorrect answer written down for a question, you will be deducted marks for the incorrect answer. If you do not wish us to look at a certain part of your solution, be sure to clearly indicate this by fully crossing it out. • Before starting your test write your name, student number, and section on this page. Questions 1 to 7

Score

Out of 7

8-10

5

11-13

5

14-16

6

17

4

18

4

19

3

20 Total

3 37

MULTIPLE-CHOICE QUESTIONS:

1. [1 point] Compute lim x→2−

(A) (F)

−5 2

(B) (G)

x+3 x−1

−2 5

(C) (H)

−1 +∞

(D) (I)

0 −∞

(E) (J)

1 DNE

(C) (H)

−1/e +∞

(D) (I)

0 −∞

(E) (J)

1/e DNE

(C) (H)

−0.02 +∞

(D) (I)

0 −∞

(E) (J)

0.02 DNE

2. [1 point] Compute lim e1−x x→∞

(A) (F)

−e 1

(B) (G)

3. [1 point] Compute lim x→0

(A) (F)

−1 0.5

(B) (G)

−1 e

sin(4x + 2) 4x + 2

−0.5 1

Page 2

FOR QUESTIONS 4-7 CONSIDER THE FUNCTION f (x) GRAPHED BELOW: 5 4 3 2 1 y = f (x)

−5 −4 −3 −2 −1 −1 −2 −3 −4 −5

1 2 3 4 5

4. [1 point] At what value(s) of x does f (x) have a removable discontinuity?

(A) (D)

−3 only −3 and 0

(B) 0 only (E) −3 and 4

(C) 4 only (F) 0 and 4

(G) −3 and 0 and 4

(H) Always continuous (I) Always discontinuous 5. [1 point] At what value(s) of x is f (x) not differentiable?

(A) (D)

−3 only −3 and 0

(B) 0 only (E) −3 and 4

(C) 4 only (F) 0 and 4

(G) −3 and 0 and 4

(H) Always differentiable (I) Never differentiable 6. [1 point] Determine the value(s) of a such that lim f (x) = 0. x→a

(A) (D)

0 only 0 and 2

(B) (E)

2 only 0 and 4

(C) 4 only (F) 2 and 4

(G) 0 and 2 and 4

(H) The limit is never 0. (I) The limit is always 0. 7. [1 point] At what value(s) of x does f ′ (x) = 0.

(A) (D)

0 only 3 only

(B) (E)

1 only 4 only

(H) 0 and 2 and 4 (I) The derivative is always 0.

(C) 2 only (F) 0 and 2

(G) 1 and 3

(J) The derivative is never 0.

Page 3

SHORT ANSWER QUESTIONS: You must show work to justify each of your answers. Answers without any justification may receive no marks.

8. [1 point] Compute lim cos(πx) +

√

x + 7.

x→2

9. [2 points] Compute lim

x→6+

10. [2 points] Compute lim x→0

4(6 − x) . |6 − x|

1−

√

1+x . x

Page 4

11. [1 point] Compute lim

x→−1+

12. [2 points] Compute lim x→−5

13. [2 points] Compute lim x→∞

−2 . x+1

tan(x + 5) . + 3x − 10

x2

−9x3 + 21 . 5x3 − 7x2 + 3x + 2

Page 5

14. [2 points] Suppose you know a function f (x) is continuous on (−∞, ∞) and that f (x) 3 ≤ f (x) ≤ 11 for all x. Determine lim . x→−∞ x4

( ln(x + 1) + 1, x ≥ 0 15. [2 points] Determine for what value(s) of k the function f (x) = kex − 6, x...